# How do you simplify (1/4)^(-1/2) ?

May 13, 2017

$2$

#### Explanation:

We can rewrite this expression as:

${1}^{- \frac{1}{2}} / {4}^{- \frac{1}{2}}$

Since they have a negative sign, flip the fraction and change the exponents positive:

${4}^{\frac{1}{2}} / {1}^{\frac{1}{2}}$

We can then also rewrite it as:

$\frac{\sqrt{4}}{\sqrt{1}} \implies 2$

May 13, 2017

See a solution process below:

#### Explanation:

First, use these two rules of exponents to rewrite the expression:

$a = {a}^{\textcolor{red}{1}}$ and ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left(\frac{1}{4}\right)}^{- \frac{1}{2}} \implies {\left({1}^{\textcolor{red}{1}} / {4}^{\textcolor{red}{1}}\right)}^{\textcolor{b l u e}{- \frac{1}{2}}} \implies {1}^{\textcolor{red}{1} \times \textcolor{b l u e}{- \frac{1}{2}}} / {4}^{\textcolor{red}{1} \times \textcolor{b l u e}{- \frac{1}{2}}} \implies$

${1}^{- \frac{1}{2}} / {4}^{- \frac{1}{2}}$

Now, use these rules of exponents to eliminate the negative exponents:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$ and $\frac{1}{x} ^ \textcolor{red}{a} = {x}^{\textcolor{red}{- a}}$

${1}^{- \frac{1}{2}} / {4}^{- \frac{1}{2}} \implies {4}^{- - \frac{1}{2}} / {1}^{- - \frac{1}{2}} \implies {4}^{\frac{1}{2}} / {1}^{\frac{1}{2}} \implies \frac{\sqrt{4}}{\sqrt{1}} \implies \frac{2}{1} \implies 2$